Shouldn't that be 'oculos aperientes' with both in Acc. Pl. The text given by Orberg has 'oculos' in Acc. Pl. and 'aperiens' in nominative singular...yet 'aperiens' is (I think!!) qualifying 'oculos'....?????

2) 'Hora prima est' inquit Davus

'Hora prima' seems to be in nominative case. I take it that stating time-when in ablative doesn't apply to 'Hora Prima est' ...?? Is that right?

I take it that 'atque etiam' means something like '...and then he washes his ears and his hair'.? What's the significance of using 'atque etiam' as opposed to 'atque et'.. when 'et.....et...' signifies 'both one thing and another thing'. ? Is it more emphasis on 'then...he did x.....'

4) Marcus caput et manus tergens Davum interrogat.

See 1) above. Manus is Nominative plural yet the agreeing 'tergens' is Nominative singular. Is this a mistake?

I take it that 'exspectantes' is masculine nominative plural to agree with 'parentes'. Is this a case of a verbal use of the participle - there's no actual verb in this clause beginning with 'ubi....' ??

6) 'hodie' is an abbreviation of 'hoc die' - which is ablative, right?

1 and 4) aperiens and tergens here are participles, so they're actually modifying "Marcus" in each case, and the words you think they're modifying are actually their object - it's not his eyes that are opening or his hands drying (for which Latin, unlike English, would have to use the passive - and there's no present passive participle) but Marcus who's opening his eyes.

5) A participle is always verbal, in a sense - it's a verbal adjective and can take objects and adverbs - but you'll rarely if ever see it actually replacing a verb. sedent is the verb in the clause you give - liberos expectantes just acts as an adjective, giving more information about what the parentes are doing while they sedent.

--Time questions---

2) Yes, it's nominative - time with the ablative expresses 'time at which' the rest of the sentence happened, but if that's not what you're expressing, you don't use it. "On Sunday, I posted a message" would have "On Sunday" as ablative, "I" as nominative and so forth, but "It's Sunday" would be nominative.

6) Yes, hoc die is ablative of 'time at which' - "on this day" but you can usually just use hodie as an adverb without the grammar mattering.

--Bathtime questions--

3) I think it just means "and even" here (atque presumably chosen because et etiam sounds weird). It's probably worth remembering that washing one's ears might be more worthy of an etiam for the Romans than for us!

Shouldn't that be 'oculos aperientes' with both in Acc. Pl. The text given by Orberg has 'oculos' in Acc. Pl. and 'aperiens' in nominative singular...yet 'aperiens' is (I think!!) qualifying 'oculos'....?????

"Marcus, opening his eyes, sees the slave." It is not the eyes that are opening. It is Marcus that opens his eyes. So the present participle agrees with Marcus, and "oculos" is its object.

2) 'Hora prima est' inquit Davus

'Hora prima' seems to be in nominative case. I take it that stating time-when in ablative doesn't apply to 'Hora Prima est' ...?? Is that right?

I take it that 'atque etiam' means something like '...and then he washes his ears and his hair'.? What's the significance of using 'atque etiam' as opposed to 'atque et'.. when 'et.....et...' signifies 'both one thing and another thing'. ? Is it more emphasis on 'then...he did x.....'

As I read it, without seeing the context, I would say that it means that he did not only wash his face: he put his whole head under water and washed even his ears and hair.

4) Marcus caput et manus tergens Davum interrogat.

See 1) above. Manus is Nominative plural yet the agreeing 'tergens' is Nominative singular. Is this a mistake?

Again, it is Marcus that is drying his head and hands. It is not the head and the hands that are drying. Say if you want a more in-depth explanation.

I take it that 'exspectantes' is masculine nominative plural to agree with 'parentes'. Is this a case of a verbal use of the participle - there's no actual verb in this clause beginning with 'ubi....' ??

Yes there is a verb; I think you should be able to spot it if you look again. If not, how would you translate this sentence?

6) 'hodie' is an abbreviation of 'hoc die' - which is ablative, right?

Originally, yes. But 'hodie' has become a fixed word that probably is better analyzed as an adverb.